Solving Complex Inequality: t > (1/2) + a / |w|^2

[eckiller]

Hello,

I have the inequality

t > (1/2) + a / |w|^2

where w is a complex number, w = a + bi. So the a in the inequality is the
real part.

So I need to find t such that all w are in a sector around the negative real
axis. Note t in [0, 1].

I am having trouble figuring out the condition to impose.


For example, before I wanted to find t such that the entire negative half of the complex plane satisfied the above inequality. t > 1/2 clearly satisfied this. Now I want to find t such that a sector around the negative real
axis satisfies the above inequality.

 

[fresh_42]

I do not understand your description but $t>\dfrac{1}{2}+\dfrac{a}{a^2+b^2}$ which means for $t\in [0,1]$that $-\dfrac{1}{2} < \dfrac{a}{a^2+b^2}< \dfrac{1}{2}\,.$ Now you can go on with whatever your condition on $w$ is.